### Abstract

Fuzzy extractors (Dodis et al., Eurocrypt 2004) convert repeated noisy readings of a secret into the same uniformly distributed key. To eliminate noise, they require an initial enrollment phase that takes the first noisy reading of the secret and produces a nonsecret helper string to be used in subsequent readings. Reusable fuzzy extractors (Boyen, CCS 2004) remain secure even when this initial enrollment phase is repeated multiple times with noisy versions of the same secret, producing multiple helper strings (for example, when a single person’s biometric is enrolled with multiple unrelated organizations). We construct the first reusable fuzzy extractor that makes no assumptions about how multiple readings of the source are correlated (the only prior construction assumed a very specific, unrealistic class of correlations). The extractor works for binary strings with Hamming noise; it achieves computational security under assumptions on the security of hash functions or in the random oracle model. It is simple and efficient and tolerates near-linear error rates. Our reusable extractor is secure for source distributions of linear min-entropy rate. The construction is also secure for sources with much lower entropy rates—lower than those supported by prior (nonreusable) constructions—assuming that the distribution has some additional structure, namely, that random subsequences of the source have sufficient minentropy. We show that such structural assumptions are necessary to support low entropy rates. We then explore further how different structural properties of a noisy source can be used to construct fuzzy extractors when the error rates are high, building a computationally secure and an information-theoretically secure construction for large-alphabet sources.

Original language | English (US) |
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Title of host publication | Advances in Cryptology - EUROCRYPT 2016 - 35th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Proceedings |

Editors | Jean-Sebastien Coron, Marc Fischlin |

Publisher | Springer Verlag |

Pages | 117-146 |

Number of pages | 30 |

ISBN (Print) | 9783662498897 |

DOIs | |

State | Published - Jan 1 2016 |

Event | 35th Annual International Conference on Theory and Applications of Cryptographic Techniques, EUROCRYPT 2016 - Vienna, Austria Duration: May 8 2016 → May 12 2016 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 9665 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 35th Annual International Conference on Theory and Applications of Cryptographic Techniques, EUROCRYPT 2016 |
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Country | Austria |

City | Vienna |

Period | 5/8/16 → 5/12/16 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Advances in Cryptology - EUROCRYPT 2016 - 35th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Proceedings*(pp. 117-146). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9665). Springer Verlag. https://doi.org/10.1007/978-3-662-49890-3_5

}

*Advances in Cryptology - EUROCRYPT 2016 - 35th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9665, Springer Verlag, pp. 117-146, 35th Annual International Conference on Theory and Applications of Cryptographic Techniques, EUROCRYPT 2016, Vienna, Austria, 5/8/16. https://doi.org/10.1007/978-3-662-49890-3_5

**Reusable fuzzy extractors for low-entropy distributions.** / Canetti, Ran; Fuller, Benjamin; Paneth, Omer; Reyzin, Leonid; Smith, Adam Davison.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Reusable fuzzy extractors for low-entropy distributions

AU - Canetti, Ran

AU - Fuller, Benjamin

AU - Paneth, Omer

AU - Reyzin, Leonid

AU - Smith, Adam Davison

PY - 2016/1/1

Y1 - 2016/1/1

N2 - Fuzzy extractors (Dodis et al., Eurocrypt 2004) convert repeated noisy readings of a secret into the same uniformly distributed key. To eliminate noise, they require an initial enrollment phase that takes the first noisy reading of the secret and produces a nonsecret helper string to be used in subsequent readings. Reusable fuzzy extractors (Boyen, CCS 2004) remain secure even when this initial enrollment phase is repeated multiple times with noisy versions of the same secret, producing multiple helper strings (for example, when a single person’s biometric is enrolled with multiple unrelated organizations). We construct the first reusable fuzzy extractor that makes no assumptions about how multiple readings of the source are correlated (the only prior construction assumed a very specific, unrealistic class of correlations). The extractor works for binary strings with Hamming noise; it achieves computational security under assumptions on the security of hash functions or in the random oracle model. It is simple and efficient and tolerates near-linear error rates. Our reusable extractor is secure for source distributions of linear min-entropy rate. The construction is also secure for sources with much lower entropy rates—lower than those supported by prior (nonreusable) constructions—assuming that the distribution has some additional structure, namely, that random subsequences of the source have sufficient minentropy. We show that such structural assumptions are necessary to support low entropy rates. We then explore further how different structural properties of a noisy source can be used to construct fuzzy extractors when the error rates are high, building a computationally secure and an information-theoretically secure construction for large-alphabet sources.

AB - Fuzzy extractors (Dodis et al., Eurocrypt 2004) convert repeated noisy readings of a secret into the same uniformly distributed key. To eliminate noise, they require an initial enrollment phase that takes the first noisy reading of the secret and produces a nonsecret helper string to be used in subsequent readings. Reusable fuzzy extractors (Boyen, CCS 2004) remain secure even when this initial enrollment phase is repeated multiple times with noisy versions of the same secret, producing multiple helper strings (for example, when a single person’s biometric is enrolled with multiple unrelated organizations). We construct the first reusable fuzzy extractor that makes no assumptions about how multiple readings of the source are correlated (the only prior construction assumed a very specific, unrealistic class of correlations). The extractor works for binary strings with Hamming noise; it achieves computational security under assumptions on the security of hash functions or in the random oracle model. It is simple and efficient and tolerates near-linear error rates. Our reusable extractor is secure for source distributions of linear min-entropy rate. The construction is also secure for sources with much lower entropy rates—lower than those supported by prior (nonreusable) constructions—assuming that the distribution has some additional structure, namely, that random subsequences of the source have sufficient minentropy. We show that such structural assumptions are necessary to support low entropy rates. We then explore further how different structural properties of a noisy source can be used to construct fuzzy extractors when the error rates are high, building a computationally secure and an information-theoretically secure construction for large-alphabet sources.

UR - http://www.scopus.com/inward/record.url?scp=84979076116&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84979076116&partnerID=8YFLogxK

U2 - 10.1007/978-3-662-49890-3_5

DO - 10.1007/978-3-662-49890-3_5

M3 - Conference contribution

AN - SCOPUS:84979076116

SN - 9783662498897

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 117

EP - 146

BT - Advances in Cryptology - EUROCRYPT 2016 - 35th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Proceedings

A2 - Coron, Jean-Sebastien

A2 - Fischlin, Marc

PB - Springer Verlag

ER -